when should you promote your pawn into a knight

It took you six months to realise this?

I looked at a knight promotion as well, but then there's the a4 escape square (and promotion of Black's pawn is also not forced).

In the early days of their chess - most players are not thinking about underpromotions.
Unfortunately - they're often struggling with openings - or otherwise not knowing what to do when their opponent makes unfamiliar opening moves.  So that's what the attention is so often on.  Or on the critical phases of middlegames.  Endgames get some attention - but not underpromotions.
Its unfortunate - because the game doesn't need to present in quite that way.  

"I looked at a knight promotion as well, but then there's the a4 escape square (and promotion of Black's pawn is also not forced)."

Its all in that nasty little passed black pawn at d2 and what white's going to do about that.  Everything else is secondary.

That's beautiful. K takes N, then advance h pawn 1 sq at a time . promote to N and come to a5 with Bl Q on a1, Nxc3 = mate.

that's Nxb3 sorry

Underpromote to knight if it controls or attacks critical squares.

https://www.chess.com/games/view/208351

That looks like it works - yes with Nxb3# is mate ...
but couldn't that be done from c5 also ?  Nxc5.
the white knight at h8 will reach a5 or c5 in the same number of moves.  Four.  No big deal though.

#30 and #31 I am confused isn't KxN stalemat?

Black queen will oscillate between a1 and a2.

But we need to chip away the layer of pawns one at a time first, because the pawn on c4 is protecting the pawn on b3.

O my bad!

Something like this, maybe? (Unless I missed something)

One of the scenarios where Stockfish does not appreciate the position well.

If white promotes to a queen, black will to and after queen takes queen, it is stalemate. Anything else than promoting to a rook/queen looses

Which is key.

Nxb3# is the key.
And its been rightly pointed out that the pawn at c4 has to be gotten rid of first.  Lol !
But what about the pawn at c5 too?  Is that to come off early - just before the mate move?  We don't want it moving later and messing things up.  Unless its going to have to be laboriously picked off too.
The idea of chipping away at black's rear pawns - is what I saw first and then I forgot about it.
Again - is b3 going to be hit from a5 or from c5 ?

1.d4 d5 2.c4 e5 3.dxe5 d4 4.e3 Bb4+ 5.Bd2 dxe3 6.Bxb4 exf2+ 7.Ke2 fxg1=N+ 8.Rxg1 Bg4+